Efficiency considerations for indefinite integration by transformation rules

Authors:
Albert D. Rich;David J. Jeffrey
Affiliations:
-;The University of Western Ontario, Department of Applied Mathematics, London, Ontario, Canada
Venue:
ISTASC'09 Proceedings of the 9th WSEAS International Conference on Systems Theory and Scientific Computation
Year:
2009

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Abstract

This paper considers the evaluation of indefinite integrals by transformation rules. The transformation rules are contained in a repository of mathematical information, and encapsulate not only knowledge of standard transformations, but also - and more importantly - conditions under which a transformation should be applied. It is precisely the conditions of application which determine the efficiency of integration. We describe, using examples, how the efficiency of the repository can be optimized to reduce the expression size of output results and to reduce the amount of computation required for a particular class of integrals.